a car go on 54kmph . the driver see a person about 46m .Then the driver click the stop bottom . the car stop 1m a front of the people. what is the time to stop it ?
To determine the time it takes for the car to stop, we need to calculate the deceleration of the car.
First, let's convert the car's speed from kilometers per hour to meters per second.
54 km/h = 54,000 m/3600 s = 15 m/s (rounded to two decimal places)
Now, we can calculate the acceleration (deceleration) of the car using the formula:
a = (vf - vi) / t
where "a" is the acceleration (deceleration) in meters per second squared, "vf" is the final velocity (0 m/s since the car stops), "vi" is the initial velocity (15 m/s), and "t" is the time it takes to stop.
Since the car stops 1 meter in front of the person, the displacement (distance) covered by the car while stopping is 46 + 1 = 47 meters. Note that the displacement is the difference between the initial and final positions.
Let's use the equation of motion:
vf^2 = vi^2 + 2ad
where "vf" is the final velocity (0 m/s), "vi" is the initial velocity (15 m/s), "a" is the acceleration (deceleration), and "d" is the displacement.
Plugging in the values:
0 = (15)^2 + 2ad
225 = 2ad
Now, substitute the value of displacement (d) as 47 meters:
225 = 2a * 47
225 = 94a
a ≈ 2.39 m/s^2 (rounded to two decimal places)
Finally, we can calculate the time (t) using the formula:
t = (vf - vi) / a
Plugging in the values:
t = (0 - 15) / (-2.39)
t ≈ 6.28 seconds (rounded to two decimal places)
Therefore, it takes approximately 6.28 seconds for the car to stop.